User blog:Nayuta Ito/My arrow notation, which supposed to be Γ 0
ERROR: THIS IS A MESS. It is an extension of chained arrow notation. Actually, arrows are not used. They all turned into arrays. First Extension X_1,X_2 is an array and Y is an array of (0 or more) 1's. a,b,c are integers more than 1 (excluding 1). If the multiple rules can be applied, the earlier one is more prior. aX_1=a a,bY=a\rightarrow b a,bY,c,X_2=ab,c-1,X_2 ,where there are b a's and as many b's as the length of Y. X_1,1X_2=X_1X_2 X_1,1,aX_2=X_1X_2 X_1,a,bX_2=[X_1,(X_1,x-1,bX_2),b-1]X_2 Googolosism: Rame Number= 8,2,55,33444,8,33,2,7777,999 Second Extension X_1,X_2 is an array, Y_1 is an array of 1 or more 1's, Y_2 is an array of 0 or more 1's, Z and Z_2 are separators (including comma). If the multiple rules can be applied, the earlier one is more prior. aX_1=a a,b1=a\rightarrow b a,bXZ1=a,bX a,bcZX=ac-1ZX ,where there are b a's and as many b's as the length of Y_2. a,bY_2,cZX=a,bb,c-1ZX ,where there are b a's and as many b's as the length of Y_2. a,bY_1ZY_2cZ_2X_2=a,bb,c-1Z_2X_2 ,where there are b b's. a,bY_1ZcZ_2X_2=a,bZ'bZ'c-1Z_2X_2 ,where there are b b's. X_1,1X_2=X_1X_2 X_1,1,aX_2=X_1X_2 X_1,a,bX_2=[X_1,(X_1,x-1,bX_2),b-1]X_2 n'=n-1 nZX'=n-1ZX Y_2,cZX'=bc-1ZX ,where there are as many b's as the length of Y_2, and b is the value from the original array. Y_1ZcZ_2X'=Z'bZ'c-1Z_2X ,where there are as many b's as the length of Y_2, and b is the value from the original array. Googologism: Numeric Spell "Epsilon Zero" '= 3,3[1,2[3[454]3]2,1] Third Extension Now I have used two pairs of brackets so far, but from now on any number of arrays are possible. This extension is supposed to be \epsilon_0\times\omega . K is the array of 1. If the second pair from the left is other than 1, you can apply the same rule as above, just anything after the second pair doesn't change at all. So I will just write the case for when the second pair is 1: a,bK1=a,b a,bK1cZX=a,bKTc-1ZX a,bK1Y_2,cZX=a,bK1b,c-1ZX ,where there are b a's and as many b's as the length of Y_2. a,bK1Y_1ZY_2cZ_2X_2=a,bK1b,c-1Z_2X_2 ,where there are b b's. a,bK1Y_1ZcZ_2X_2=a,bK1Z'bZ'c-1Z_2X_2 ,where there are b b's. ,where T is [a[a[a \cdots ]a]a] , where there are b pairs of brackets. Googologism:'Suica Number = 3,311\cdots172 ,where there are 72 1's. Fourth Extension The array of brackets is supposed to be multidimensional. Subscripts are added in this section. This is supposed to be \epsilon_{\omega} . I will just write the additional part about what if the second brackets have a subscript. If the second brackets don't have a subscript, the same rule as above is applied. R is some array. R_S is an array of brackets which all have each subscript. No subscript is the same as the subscript of 0. a,bR_SXR=a,bR_S'XR 1'=[_{n-1}a[_{n-1}a_{n-1}\cdotsb]b] , where there are b pairs of brackets. X'=X'X'\cdotsX'L' (_{n_1}X_1_{n_2}X_2\cdots_{n_t}X_t)'=_{n_1}X_1_{n_2}X_2\cdots_{n_t}X_t' The last parenthesis is used in a "normal" meaning. It's just a binding rope. Googolosism: τεωι = 3,3_{17}820 Fifth Extension The subscripts are nested. If the subscript is a number, you can wrap it with "[]". In this part, n is an array, This is supposed to be \zeta_0 . a,bR_SXR=a,bR_S'XR 1'=[_{n'}a[_{n'}a_{n'}\cdotsb]b] , where there are b pairs of brackets. X'=X'X'\cdotsX'L' (_{n_1}X_1_{n_2}X_2\cdots_{n_t}X_t)'=_{n_1}X_1_{n_2}X_2\cdots_{n_t}X_t' The last parenthesis is used in a "normal" meaning. It's just a binding rope. Googologism: Kayn Number = 3,3[_{[_{[_{3}3]}3]}3]3 Sixth Extension Curly parentheses are added to indicate the kind of brackets. If the bracket contains anything other than 1 and parentheses, then you can use the rules above, ignoring the parentheses. This is supposed to be \Gamma_0 . No parentheses is the same as (0), (X)1'=[(X')_{_{[(X')b} \cdots}b}b] (X)'=(X') 1)1'=(_{X'}(_{X'}\cdots(_{X'}b)\cdots)b)b GOogologism: Izasige Sakuya= 16,16[(_{_{[(_{[16}16)16]} \cdots}16)16]}16)16]16 , where there are 16 layers. Category:Blog posts